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A = \(\frac{2.4.6+4.6.8+6.8.10+8.10.12+...+198.200.202}{1.3.5+3.5.7+5.7.9+7.9.11+...+97.99.101}\) =?
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\(\dfrac{3}{2.6}\) + \(\dfrac{3}{6.10}\) + \(\dfrac{3}{10.14}\)
= \(\dfrac{3}{4}\).(\(\dfrac{4}{2.6}\) + \(\dfrac{4}{6.10}\) + \(\dfrac{4}{10.14}\))
= \(\dfrac{3}{4}\).(\(\dfrac{1}{2}-\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{10}\) + \(\dfrac{1}{10}\) - \(\dfrac{1}{14}\))
= \(\dfrac{3}{4}\).(\(\dfrac{1}{2}\) - \(\dfrac{1}{14}\))
= \(\dfrac{3}{4}\). \(\dfrac{3}{7}\)
= \(\dfrac{9}{28}\)
B = \(\dfrac{4}{1.3.5}\) + \(\dfrac{4}{3.5.7}\) + \(\dfrac{4}{5.7.9}\)
B = \(\dfrac{1}{1.3}\) - \(\dfrac{1}{3.5}\) + \(\dfrac{1}{3.5}\) - \(\dfrac{1}{5.7}\) + \(\dfrac{1}{5.7}\) - \(\dfrac{1}{7.9}\)
B = \(\dfrac{1}{1.3}\) - \(\dfrac{1}{7.9}\)
B = \(\dfrac{1}{3}\) - \(\dfrac{1}{63}\)
B = \(\dfrac{20}{63}\)
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\(A=\dfrac{2.6.10+6.10.14+10.14.18+..+194.198.202}{1.3.5+3.5.7+5.7.9+..+97.99.101}\)
\(=\dfrac{2^3.1.3.5+2^3.3.5.7+2^3.5.7.9+...+2^3.97.99.101}{1.3.5+3.5.7+7.9.11+...+97.99.101}\)
\(=\dfrac{2^3.\left(1.3.5+3.5.7+7.9.11+...+97.99.101\right)}{1.3.5+3.5.7+5.7.9+...+97.99.101}=2^3=8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có tử =2.(1.3.5)+2.(3.5.7)+2.(5.7.9)+....+2.(97.99.101)
=2.(1.3.5+3.5.7+5.7.9+....+97.99.101)
mà mẫu =1.3.5+3.5.7+5.7.9+...+97.99.101
suy ra A=2
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